#include "libm.h"
static const float
-tiny = 1e-30,
-half = 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
-/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
+static float erfc1(float x)
+{
+ float_t s,P,Q;
+
+ s = fabsf(x) - 1;
+ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
+ Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+ return 1 - erx - P/Q;
+}
+
+static float erfc2(uint32_t ix, float x)
+{
+ float_t s,R,S;
+ float z;
+
+ if (ix < 0x3fa00000) /* |x| < 1.25 */
+ return erfc1(x);
+
+ x = fabsf(x);
+ s = 1/(x*x);
+ if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
+ R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
+ ra5+s*(ra6+s*ra7))))));
+ S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
+ sa5+s*(sa6+s*(sa7+s*sa8)))))));
+ } else { /* |x| >= 1/0.35 */
+ R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
+ rb5+s*rb6)))));
+ S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
+ sb5+s*(sb6+s*sb7))))));
+ }
+ GET_FLOAT_WORD(ix, x);
+ SET_FLOAT_WORD(z, ix&0xffffe000);
+ return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x;
+}
+
float erff(float x)
{
- int32_t hx,ix,i;
- float R,S,P,Q,s,y,z,r;
+ float r,s,z,y;
+ uint32_t ix;
+ int sign;
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff;
+ GET_FLOAT_WORD(ix, x);
+ sign = ix>>31;
+ ix &= 0x7fffffff;
if (ix >= 0x7f800000) {
/* erf(nan)=nan, erf(+-inf)=+-1 */
- i = ((uint32_t)hx>>31)<<1;
- return (float)(1-i)+one/x;
+ return 1-2*sign + 1/x;
}
if (ix < 0x3f580000) { /* |x| < 0.84375 */
if (ix < 0x31800000) { /* |x| < 2**-28 */
- if (ix < 0x04000000)
- /*avoid underflow */
- return 0.125f*(8.0f*x + efx8*x);
- return x + efx*x;
+ /*avoid underflow */
+ return 0.125f*(8*x + efx8*x);
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
- s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+ s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
- if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = fabsf(x)-one;
- P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
- Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
- if (hx >= 0)
- return erx + P/Q;
- return -erx - P/Q;
- }
- if (ix >= 0x40c00000) { /* inf > |x| >= 6 */
- if (hx >= 0)
- return one - tiny;
- return tiny - one;
- }
- x = fabsf(x);
- s = one/(x*x);
- if (ix < 0x4036DB6E) { /* |x| < 1/0.35 */
- R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
- ra5+s*(ra6+s*ra7))))));
- S = one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
- sa5+s*(sa6+s*(sa7+s*sa8)))))));
- } else { /* |x| >= 1/0.35 */
- R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
- rb5+s*rb6)))));
- S = one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
- sb5+s*(sb6+s*sb7))))));
- }
- GET_FLOAT_WORD(ix, x);
- SET_FLOAT_WORD(z, ix&0xfffff000);
- r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
- if (hx >= 0)
- return one - r/x;
- return r/x - one;
+ if (ix < 0x40c00000) /* |x| < 6 */
+ y = 1 - erfc2(ix,x);
+ else
+ y = 1 - 0x1p-120f;
+ return sign ? -y : y;
}
float erfcf(float x)
{
- int32_t hx,ix;
- float R,S,P,Q,s,y,z,r;
+ float r,s,z,y;
+ uint32_t ix;
+ int sign;
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff;
+ GET_FLOAT_WORD(ix, x);
+ sign = ix>>31;
+ ix &= 0x7fffffff;
if (ix >= 0x7f800000) {
/* erfc(nan)=nan, erfc(+-inf)=0,2 */
- return (float)(((uint32_t)hx>>31)<<1) + one/x;
+ return 2*sign + 1/x;
}
if (ix < 0x3f580000) { /* |x| < 0.84375 */
if (ix < 0x23800000) /* |x| < 2**-56 */
- return one - x;
+ return 1.0f - x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
- s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+ s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
- if (hx < 0x3e800000) { /* x<1/4 */
- return one - (x+x*y);
- } else {
- r = x*y;
- r += (x-half);
- return half - r ;
- }
- }
- if (ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
- s = fabsf(x)-one;
- P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
- Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
- if(hx >= 0) {
- z = one - erx;
- return z - P/Q;
- } else {
- z = erx + P/Q;
- return one + z;
- }
+ if (sign || ix < 0x3e800000) /* x < 1/4 */
+ return 1.0f - (x+x*y);
+ return 0.5f - (x - 0.5f + x*y);
}
if (ix < 0x41e00000) { /* |x| < 28 */
- x = fabsf(x);
- s = one/(x*x);
- if (ix < 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
- ra5+s*(ra6+s*ra7))))));
- S = one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
- sa5+s*(sa6+s*(sa7+s*sa8)))))));
- } else { /* |x| >= 1/.35 ~ 2.857143 */
- if (hx < 0 && ix >= 0x40c00000) /* x < -6 */
- return two-tiny;
- R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
- rb5+s*rb6)))));
- S = one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
- sb5+s*(sb6+s*sb7))))));
- }
- GET_FLOAT_WORD(ix, x);
- SET_FLOAT_WORD(z, ix&0xfffff000);
- r = expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S);
- if (hx > 0)
- return r/x;
- return two - r/x;
+ return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
}
- if (hx > 0)
- return tiny*tiny;
- return two - tiny;
+ return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f;
}
projects / musl / blobdiff